Applied Mori theory of the moduli space of stable pointed rational curves [Elektronische Ressource] / Paul L. Larsen. Gutachter: Klaus Altmann ; Gavril Farkas ; Angela Gibney

Applied Mori theory of the moduli space of stablepointed rational curvesDISSERTATIONzur Erlangung des akademischen GradesDr. rer. nat.im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonPaul L. Larsen M.Sc., B.A., B.S.Präsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Peter FrenschGutachter:(i) Prof. Dr. Klaus Altmann(ii) Prof. Dr. Gavril Farkas(iii)Prof. Dr. Angela Gibneyeingereicht am: 21. Juli 2010Tag der mündlichen Prüfung: 9. November 2010To my grandparents, Wilbur and Cleta.AcknowledgmentsI would like to thank my advisor, Gavril Farkas, first and foremost. His wealth of ideasand explanations, as well as his support across two continents of thesis work, have beeninvaluable. I am indebted to several mathematicians, conversations with whom helpedshape the three main parts of this thesis. Chapter 2 on Fulton’s conjecture benefittedfrom conversations with Frank Sottile and Günter Ziegler, the role of toric geometryin Chapters 3 and 4 originated in conversations with Nathan Ilten, who also answeredinnumerable questions about toric geometry, and input from Sam Payne on Chapter 4led to several improvements.I am very fortunate to have benefitted from the supportive and productive atmosphereof the mathematics departments at the University of Texas at Austin, where my Ph.D.